Random Fields

Abstract

In this chapter we look at the topics of chapters C and D — extrema and boundary crossings — for d-parameter processes instead of 1-parameter processes. A random field X(t) or Xt is just a real-valued process parametrized by t = (t1,...,td) in Rd or some subset of Rd. Since this concept may be less familiar to the reader than earlier types of random process, let us start by mentioning several contexts where random fields arise.